I only have a couple of things to add to Thai-Kiwi's post which seems to me to show that on Star Alliance website there is no prohibition on accruing to one program and gaining lounge access via a different one. In fact, I queried Air NZ as to whether this was allowed with programmes outside Airpoints and was told that it was. Subsequently I have done this (credited a NZ flight to a non-NZ Star Alliance airline, whilst using my gold card from a different airline to obtain access to the lounge) at Air NZ lounges in AKL and WLG. Thus it seems to me that it is permissible, even when flying on NZ, to split FQTV and FQTS. Air NZ, however, do not like this as under section 10 of the Terms and Conditions of Airpoints it states:

When you book your travel, you may only specify one Airline's loyalty programme or frequent flyer programme in your booking. Your loyalty or frequent flyer points will be credited to your chosen programme and you may only access the benefits of the chosen programme for that travel. For example, you cannot earn Airpoints Dollars or Status Points and use the benefits of another Airline's loyalty programme or frequent flyer programme. In addition, you cannot use the benefits of the Airpoints programme and earn loyalty or frequent flyer points with another programme.

This section is incompatible with what's on the Star Alliance website. The problem is not that NZ is unable to credit to one programme whilst the passenger is obtaining benefits from another: it just doesn't want to when Airpoints is involved.